Computer turns on for only a sec

Hi,

I'v had an alienware 14 for over 3 years now. I'm really happy with it but recently i'v had a few problems. The first one was that out of my 16gb or ram it started to only detect 8gb I never solved this problem but it didnt bother me. The second problem which i'm having right now is that my pc won"t turn on. I explain: I was playing league of legend, about 5 min in game, my pc doesn't have any heat issues. It suddenly instantly turned off. I was pretty surprise but didn't think it was much. What you also have to known is that my battery is pretty much almost dead, which I was planning on ordering a new one ( it last for like 20 min ) but when playing plugged in it doesnt bother me much. The second thing to know is that I once broke a little plastic clipper used to plug the optical drive. I fixed it by using a little piece of card that I put in the whole ( this works really good ). Back to the prob, I turn on my pc back on, lights are on, i hear the fans turning and the little disk noise that alienware makes when you turn it on but then it just shuts off. The screen stays black. At first i'm a bit confused so after trying to turn it on a few times I deciced to open it to see what was going on. The optical drive moved a little bit so I thought that was the prob so i fixed it and plugged it back. Then hurrey pc screen turns on, i get the alienware logo but then it shuts off. Im pretty tired and deciced to go to bed and give it a try next morning. The morning i try switching the ram sticks and I turn on the pc without the battery. Hurrey ! I get passed the alienware logo and even get on my pc. My desktop seems fine, no files is missing, i'm a happy man. But then it just shuts off, again. Now im stucked with a pc that turns on for 2 sec with nothing but a black screen. Lights are ok, fans ok and i still hear that little noise that i'v always heard.

If you made it passed here congrats, and thank you for reading my post. I would really appreciated if someone could help me out :)

friendly, Malo